Estimating the size of a closed population by modeling latent and observed heterogeneity

We describe a new class of capture-recapture models for closed populations when individual covariates are available. The novelty consists in combining a latent class model where the marginal weights and the conditional distributions given the latent may depend on covariates, with a model for the marginal distribution of the available covariates. In addition, a general formulation for the conditional distributions given the latent which allows serial dependence is provided. An efficient algorithm for maximum likelihood estimation is presented, asymptotic results are derived, and a procedure for constructing likelihood based confidence intervals for the population total is presented. Two examples with real data are used to illustrate the proposed approach.